Question

The relation between an ac voltage source and time in $SI$ units is $V= 120\, sin(100 \,\pi t)cos(100\,\pi t) V$. The value of peak voltage and frequency will be respectively

• A. $120\,V$ and $100 \,Hz$
• B. $\frac{120}{\sqrt{2}}V$ and $100 \,Hz$
• C. $60\,V$ and $200 \,Hz$
• D. $60\,V$ and $100 \,Hz$

Answer 1

Answer: (D)

$60\,V$ and $100 \,Hz$

Answer 2

$V= 120\, sin(100\pi t)cos(100 \pi t) V$ $= 60\, sin(200 \pi t) V (\because sin2\theta = 2 sin\theta cos\theta)$ Compare it with standard equation, $V = V_0\, sin\omega t$ We get, $V_0 = 60\,V$ and $\omega=200\pi$ or $2\pi\upsilon =200\pi$ or $\upsilon=100\,Hz$